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The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z+4=0 and parallel to x-axis is

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Important Questions on Three Dimensional Geometry

MEDIUM
The equation of the plane passing through the line of intersection of the planes r·2i^-3j^+4k^=1 and r·i^-j^+4=0 and perpendicular to the plane r·2i^-j^-k^+4=0, is
MEDIUM
The equation of the plane containing the line of intersection of 2x-5y+z=3; x+y+4z=5, and parallel to the plane, x+3y+6z=1, is
EASY
If the equation of the plane passing through the line of intersection of the planes 2x-7y+4z-3=0, 3x-5y+4z+11=0 and the point -2, 1, 3 is ax+by+cz-7=0, then the value of 2a+b+c-7 is _________.
MEDIUM
Let the equation of the plane, that passes through the point (1,4,-3) and contains the line of intersection of the planes 3 x-2 y+4 z-7=0 and x+5 y-2 z+9=0, be αx+βy+γz+3=0, then α+β+γ is equal to :
MEDIUM
The equation of the plane passing through the intersection of the planes x+2y-z=3 and x+y-3z=5 and passing through the point (1,-1,0) is
MEDIUM
Equation of a plane at a distance 221 units from the origin, which contains the line of intersection of the planes x-y-z-1=0 and 2x+y-3 z+4=0, is
MEDIUM
The vector equation of the plane passing through the intersection of the planes r·i^+j^+k^=1 and r·i^-2j^=-2, and the point 1, 0, 2 is:
MEDIUM
The equation of the plane passing through the line of intersection of the planes x+y+z=6 and 2 x+3 y+4 z+5=0 and passing through (1,1,1) is
MEDIUM
If the equation of a plane P, passing through the intersection of the planes, x+4y-z+7=0 and 3x+y+5z=8 is ax+by+6z=15 for some a,bR, then the distance of the point 3,2,-1 from the plane P is
MEDIUM
The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z+4=0 and parallel to X-axis is
EASY
The vector in the direction of the sum of the vectors a=2i^-2j^+5k^ and b=-2i^+5j^-3k^ is
MEDIUM
The equation of a plane containing the line of intersection of the planes 2x-y-4=0 and y+2z-4=0 and passing through the point 1,1,0 is
MEDIUM
X intercept of the plane containing the line of intersection of the planes x-2y+z+2=0 and 3x-y-z+1=0 and also passing through (1,1,1) is
MEDIUM
A plane P contains the line x+2y+3 z+1=0=x-y-z-6, and is perpendicular to the plane -2x+y+z+8=0. Then which of the following points lies on P?
MEDIUM
The equation of the plane passing through the line of intersection of the planes r·(i^+j^+k^)=1 and r·(2i^+3j^-k^)+4=0 and parallel to the x-axis, is
HARD
The equation of a plane passing through the line of intersection of the planes x+2y+3z=2 and xy+z=3 and at a distance 23 from the point 3, 1, -1 is -
MEDIUM
The vector equation of a plane passing through the line of intersection of the planes r·n1=q1 and r·n2=q2 is 
MEDIUM
Determine the plane through the intersection of the planes x+2y+3z-4=0 and 2x+y-z+5=0 and perpendicular to the plane 5x+3y+6z+8=0
MEDIUM
The vector equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0 is
EASY
Let P be the plane, which contains the line of intersection of the planes, x+y+z-6=0 and 2x+3y+z+5=0 and it is perpendicular to the xy-plane. Then the distance of the point 0, 0, 256 from P is equal to: